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Some characterizations for the exponential \(\varphi\)-expansiveness of linear skew-product semiflows. (Chinese. English summary) Zbl 1499.37021

Summary: The exponential \(\varphi\)-expansiveness of linear skew-product semiflows in Banach space was studied. Based on the definition of uniform exponential expansiveness, a linear skew-product semiflow with exponential \(\varphi\)-expansiveness was presented. Some characterizations for exponential \(\varphi\)-expansiveness were obtained via mathematical analysis and operator theory. The results extend some well-known conclusions in the exponential stability theory.

MSC:

37B05 Dynamical systems involving transformations and group actions with special properties (minimality, distality, proximality, expansivity, etc.)
37C10 Dynamics induced by flows and semiflows
37C75 Stability theory for smooth dynamical systems